On Disappearing H-Bridges

On Disappearing H-Bridges

Many of you have reported on the mysterious destruction of your H-Bridges. Some of that can be ascribed to careless handling—touching wires together and so on. However, as I listen to the stories there seems to be a pattern of H Bridges suddenly dying after performing reliably with no-one having changed a thing or even touched anything. The one clue I picked up Saturday was that they were suddenly running very hot.

So here’s a little old fashioned engineering analysis, most of it done in my head at various times over the weekend. I’m not boasting, by the way. What I’m saying is, it’s not difficult.

Overheating is caused by power dissipation. A switching element dissipates power when it’s off, when it’s on and when it’s switching

The off power is the peak voltage times the leakage current (which should be very small) times the proportion of the time the switch is off–

where D is the duty cycle. The on power is the switched current (which we’ll call the peak current although it may vary depending upon what the motor is doing) times the switch drop times the proportion of the time it is on–

The switching power takes a little more work. Suppose the voltage goes linearly from 0 to Vpk in ts seconds while the current starts from Ipk and drops linearly to 0 in the same time. Then the instantaneous power dissipated in the switching device is

By integrating this over the switching time we can calculate the energy dissipated

Assuming the positive and negative going switching is symmetric, this occurs twice per switching cycle, so that the average power over one cycle is

The 1/6 represents a shape factor–that is it depends upon the exact shape of the currents and voltages during the rise and fall times. The details may differ (the waveforms might be more exponential, for example, and the rise and fall shapes might differ) but the only difference to the analysis is in the exact value of the shape factor.

Thus the total power dissipated in the switching element is

where the off term has been neglected as most switching devices have very low leakage currents and ksh has been used to represent the shape factor. H-Bridges are a little more complicated than a simple switching element. However, for a given direction only two arms of the bridge are used (and only one of the elements is actually turned on and off). The pair can be treated as a single element with Von equal to the total drop across both elements when they are turned on.

They also have clamp diodes for absorbing the back emf from the motors. The energy stored in the coil kicks back when the current is interrupted. Normally, that results in a major voltage spike but the clamp diodes take care of that. However, they do so by conducting current to ground and that represents more power dissipated by the H Bridge chip. Whatever that energy is (and LI2/2 tickles at my memory), it is dumped once per cycle (when the current is turned off).

where ED is the energy dumped into the clamp diodes during one cycle.

We can conclude a number of things from this equation:

1. Decreasing the switching frequency will decrease the power dissipation.
2. Doing anything to increase the switching time (for example by adding capacitance in the wring place) will increase the power dissipation.
3. Running the motors hard (increasing D) will increase the power dissipation. What a surprise!
4. Putting the motors under load will increase Ipk and increase the power dissipation (another surprise!).

What’s the effect of power dissipation? Heat sink design is predicated on modeling heat as current and temperature as voltage. Then the analog of electrical resistance is thermal resistance. The manufacturer should specify (either directly or indirectly) the thermal resistance between the inside of a chip and the case, and between the case and the ambient air, giving us the simple thermal voltage divider below.

PD represent the power dissipation in the chip. Tamb is the ambient temperature (the air temperature inside the robot next to the H-Bridge). ThetaJC is the thermal junction to case resistance and ThetaCA the thermal case to air resistance. Adding a heat sink puts another ThetaHS in parallel with ThetaCA, effectively lowering that resistance. Nothing can be done about ThetaJC which depends strictly upon the existing thermal design of the chip.

The power current flowing through the resistances raises the temperature both on the case (the T between the resistances) and at the junction. If TJ exceeds 150°C the semiconductor will fail. If one knows the ambient temperature and the case temperature you can estimate the junction temperature. However case temp is hard to measure accurately. Old timers will often wet a finger and tap it against the case. If you here a ssst, you know the case temperature exceeds a 100°C. (The moisture protects your finger against burns, as long as you touch very briefly, and the sizzle tells you it’s become instant steam.)

Remember, even if you keep everything else constant, if ambient temperature rises, the junction temperature goes up with it.

(My equation editor doesn’t have a parallel operator so I used a perpendicular to represent parallel.) So now you’ve got a way to estimate PD and to figure out the consequence in terms of worst case junction temperature. Under the worst case conditions, you really don’t want it above 125°C.

I’m willing to bet a number of you are running too close to the bone. It should be very quick to calculate it.

mpbl

25 November, 2002

Shape factors

The shape factor for a linear rise or fall is 1/6. That assumes 0 to 100% ts. If one were to use the standard 10% to 90%, the measured switching time is only .8ts, so the shape factor has to increase to compensate to 1/(.8 x 6) » .2

The maximum shape factor is 1. This would require I(t) to be Ipk and v(t) to be Vpk during the entire switching period, a blatant impossibility.

Exponential switching

If one takes the fall time to be t, the shape factor is .5. However, the 10% to 90% falltime is

Yielding a shape factor of .228 which is very close to the linear as measured with a 10%-90% falltime

Thus a reasonable working definition of worst case switching power would be

where rise and fall time are measured at the conventional 10% and 90% levels and the shape factor of .25 is close to and slightly larger than the two cases we’ve examined.